We study Kauffman's model of folded ribbon knots: knots made a thin strip paper flat in the plane. The ribbonlength is length to width ratio such knot. show for any knot or link type that there exist constants $c_1, c_2>0$ bounded above by $c_1\cdot Cr(K)^2$, and also $c_2\cdot Cr(K)^{3/2}$. use different method each bound. constant $c_1$ quite small comparison $c_2$, first bound lower than sec...

We discuss the definition of conserved quantities in asymptotically locally de Sitter spacetimes. One may define an analogue holographic charges at future and past infinity other Cauchy surfaces $I_t$ as integrals over intersection timelike $C$ surface $I_t$. In general, $Q^t$ defined on depend $C$, but if gravitational flux is absent are independent $C$. On hand, there a net entering or leavin...

We consider the identity component of Sato-Tate group Jacobian curves form $$C_1\colon y^2=x^{2g+2}+c, C_2\colon y^2=x^{2g+1}+cx, C_3\colon y^2=x^{2g+1} +c,$$ where $g$ is genus curve and $c\in\mathbb Q^*$ constant. approach this problem in three ways. First we use a theorem Kani-Rosen to determine splitting Jacobians for $C_1$ 4 5 prove what each case. then higher by finding maps lower computi...

Let ${c_1(x),c_2(x),f_1(x),f_2(x)}$ be polynomials with rational coefficients. The “obvious” exceptions being excluded, there can at most finitely many roots of unity among the zeros ${c_1(x)f_1(x)^n+c_2(x)f_2(x)^n}$ $n=1,2\ldot

As a particular problem within the field of non-autonomous discrete systems, we consider iterations two quadratic maps $$f_{c_0}=z^2+c_0$$ and $$f_{c_1}=z^2+c_1$$ , according to prescribed binary sequence, which call template. We study asymptotic behavior critical orbits define Mandelbrot set in this case as locus for these are bounded. However, unlike single maps, concept can be understood sev...

Let $${\mathcal {O}}$$ be a closed n-dimensional arithmetic (real or complex) hyperbolic orbifold. We show that the diameter of is bounded above by $$\begin{aligned} \frac{c_1\log \mathrm {vol}({\mathcal {O}}) + c_2}{h({\mathcal {O}})}, \end{aligned}$$ where $$h({\mathcal {O}})$$ Cheeger constant , $$\mathrm its volume, and constants $$c_1$$ $$c_2$$ depend only on n.

Let A and B be 2 × non-zero complex matrices. P a linear combination of in the form P=c_1 A+c_2 where c_1,c_2 are nonzero scalar numbers. An idempotent matrix is which, when multiplied by itself, yields itself. In this study, we established entries according to given such that also an matrix. addition, result was obtained determined singular

Consider two random vectors $\mathbf C_1^{1/2}\mathbf x \in \mathbb R^p$ and C_2^{1/2}\mathbf y\in R^q$, where the entries of x$ y$ are i.i.d. variables with mean zero variance one, C_1$ C_2$ $p \times p$ $q\times q$ deterministic population covariance matrices. With $n$ independent samples $(\mathbf x,\mathbf y)$, we study sample correlation between these using canonical analysis. We denote by...

The inverse problem of reconstructing a source term from boundary measurements, for the wave equation, is revisited. We propose novel approach to recover unknown through measuring fields after injecting small particles, enjoying high contrast, into medium. For this purpose, we first derive asymptotic expansion field, based on time-domain Lippmann-Schwinger equation. dominant in expressed as an ...